Limit of (1 - √(1 - 4x²))/x² as x → 0

[devious_]

I'm having trouble with the following limit:

$$\lim_{x \rightarrow 0} \frac{1 - \sqrt{1 - 4x^2}}{x^2}$$

At the back of the book (Apostol Volume I), it says the answer is 1/2, but I get 2. Can anyone clarify?

Thanks.

 

[joeboo]

multiply by 1 :
$$\frac{1 + \sqrt{1-4x^2}}{1 + \sqrt{1-4x^2}}$$

Seems to me you are correct

 

[dextercioby]

Yes,even l'Hôpital approves you guys.A typo in the book,nothing sensational.

Daniel.

 

[devious_]

Good to know. Thanks.